Statistics > Methodology

Abstract: MCMC methods are used in Bayesian statistics not only to sample from
posterior distributions but also to estimate expectations. Underlying functions
are most often defined on a continuous state space and can be unbounded. We
consider a regenerative setting and Monte Carlo estimators based on i.i.d.
blocks of a Markov chain trajectory. The main result is an inequality for the
mean square error. We also consider confidence bounds. We first derive the
results in terms of the asymptotic variance and then bound the asymptotic
variance for both uniformly ergodic and geometrically ergodic Markov chains.